Are the terms session and process totally synonymous in shell-scripting or at least in Bash?
No, they're not the same at all.
A process is a running instance of a program. It has a process id (PID), a set of virtual memory, a user id, a set of open file descriptors, and a number of other things.
The Unix concept of a session is a kernel construct related to grouping processes mostly in the context of a terminal-based login.
A session is a group of processes, itself divided to one or more process groups. The following diagram from Advanced Programming in the Unix Environment shows the relations quite well:

It should be mentioned that the session as a whole can have a controlling terminal, but the processes within it are otherwise distinct.
See:
Notes:
Of course, "session" can have other meanings not related to terminals. The concept of a login session can make sense in a GUI system or e.g. a Web-based program too, even if they didn't use terminals and process groups in the same way as a terminal-based session.
Then again, "process" has other less technical meanings too.